Short answers, pulled from the story.
The earliest existing record of a telescope is a 1608 patent submitted to the government in the Netherlands by Middelburg spectacle maker Hans Lipperhey for a refracting telescope. The actual inventor is unknown, but word spread through Europe, and Galileo Galilei built his own version in 1609.
The word telescope was coined in 1611 by the Greek mathematician Giovanni Demisiani for one of Galileo Galilei's instruments, presented at a banquet at the Accademia dei Lincei. It combines the Ancient Greek tele, meaning far, and skopein, meaning to look or see.
A refracting telescope uses lenses to form an image, while a reflecting telescope uses an arrangement of mirrors. Isaac Newton built the first practical reflecting telescope in 1668, a design now called the Newtonian reflector.
The maximum physical size limit for refracting telescopes is about one meter, so most large optical research telescopes built since the turn of the 20th century have been reflectors. The largest reflecting telescopes today have objectives larger than 10 meters, with designs of 30 to 40 meters underway.
The atmosphere is opaque to most of the electromagnetic spectrum, so X-ray and far-infrared telescopes must observe from orbit. Even for observable wavelengths, a space telescope can avoid clouds, astronomical seeing, and light pollution, though it costs more and is harder to maintain and upgrade.
The James Webb Space Telescope is a NASA space telescope that detects infrared light and orbits the L2 Lagrange Point of the earth-sun system. It launched on the 25th of December 2021 from Kourou, in French Guiana, on an Ariane 5 rocket.
X-ray telescopes use Wolter telescopes, ring-shaped glancing mirrors of heavy metals that reflect rays by just a few degrees, as on Chandra and NuSTAR. The highest-energy X-ray and gamma-ray telescopes give up focusing and use coded aperture masks, whose shadow patterns are reconstructed into an image.